DeepONet Getting Started

Path

Stage 1: Theory (1-2 days)

• DeepONet = Branch Net (encodes u(x)) + Trunk Net (encodes coordinate t), inner product gives operator G(u)(t). Rooted in Kolmogorov-Arnold representation.
• Must-read: Lu et al., "DeepONet", Nature Machine Intelligence 2021

Stage 2: DeepXDE (3-5 days)

DeepXDE (MIT) is the most mature PINN/DeepONet framework.

• Learning order: Burgers -> Porter -> SDE

Stage 3: Industrial practice

• Parametric geometry response
• Multiphysics (thermo-structural)
• Flow surrogate on the U-bend dataset

vs FNO

• Grid adaptability: DeepONet yes vs FNO no
• Parameter dimension: DeepONet high vs FNO limited
• Data efficiency: DeepONet high vs FNO requires more data
• Framework: DeepXDE yes / NeuralOperator yes

Resources

• DeepXDE docs (Chinese-friendly)
• Lu et al. 2021
• GitHub: lululxvi/deepxde